A widely adapted electronic-fuel-injection-type internal combustion engine has at least one fuel injection valve (fuel injector) at each of the cylinders or at each of intake ports communicating with each of the cylinders. Accordingly, when the characteristic/property of the fuel injection valve of a certain specific cylinder changes to inject fuel in an amount excessively larger than an instructed fuel injection amount, only an air-fuel ratio of an air-fuel mixture supplied to that certain specific cylinder greatly changes toward a rich side. Consequently, the degree of air-fuel ratio non-uniformity among the cylinders increases. In other words, there arises an imbalance among cylinder-by-cylinder air-fuel ratios, each of which is the air-fuel ratio of the air-fuel mixture supplied to each of the cylinders (that is, an inter-cylinder air-fuel ratio imbalance state occurs). The inter-cylinder air-fuel ratio imbalance state also occurs, for example, in a case where the characteristic of the fuel injection valve of the certain specific cylinder changes to inject fuel in an amount excessively smaller than the instructed fuel injection amount.
When the inter-cylinder air-fuel ratio imbalance state occurs, the air-fuel ratio of an exhaust gas greatly fluctuates. Thus, an output value of an air-fuel ratio sensor greatly fluctuates, the sensor being disposed at an exhaust merging/aggregated portion into which exhaust gases from a plurality of the cylinders of the engine merge. In view of the above, one of conventional inter-cylinder air-fuel ratio imbalance determination apparatuses obtains a trace/trajectory length of the output value of the air-fuel ratio sensor, compares the trace length with a “reference value which changes in accordance with the rotational speed of the engine,” and determines whether or not the inter-cylinder air-fuel ratio imbalance state has occurred on the basis of the result of the comparison (see, for example, U.S. Pat. No. 7,152,594).
It should be noted that, in the present specification, determining whether or not an inter-cylinder air-fuel ratio imbalance state has occurred means determining whether or not an excessive inter-cylinder air-fuel ratio imbalance state has occurred. The excessive inter-cylinder air-fuel ratio imbalance state means a state in which a difference between inter-cylinder air-fuel-ratios (cylinder-by-cylinder air-fuel ratios) is equal to or greater than a predetermined value. The determination as to whether or not the “inter-cylinder air-fuel ratio imbalance state” has occurred will be simply referred to as an “inter-cylinder air-fuel ratio imbalance determination” or “imbalance determination.” Further, a cylinder supplied with an air-fuel mixture whose air-fuel ratio deviates from the air-fuel ratio of air-fuel mixtures supplied to the remaining cylinders (typically, stoichiometric air-fuel ratio) will also be referred to as an “imbalanced cylinder.” The air-fuel ratio of the air-fuel mixture supplied to the imbalanced cylinder will also be referred to as an “air-fuel ratio of the imbalanced cylinder.” The remaining cylinders (cylinders other than the imbalanced cylinder) will also be referred to as “normal cylinders” or “balanced cylinders.” The air-fuel ratio of air-fuel mixtures supplied to the balanced cylinders will also be referred to as “air-fuel ratio of the balanced cylinders” or “air-fuel ratio of the normal cylinders”. According to those definitions, a difference between/among the cylinder-by-cylinder air-fuel ratios is a difference between “the air-fuel ratio of the imbalanced cylinder and the air-fuel ratio of the balanced cylinders”, and will be referred to as a “cylinder-by-cylinder air-fuel ratio difference.”
In addition, a parameter (e.g., the trace length of the output value of the above-mentioned air-fuel ratio sensor), which is obtained based on the output value of the air-fuel ratio sensor, which reflects (varies depending on) a “magnitude of the fluctuation of the exhaust gas air-fuel ratio which increases as the cylinder-by-cylinder air-fuel ratio difference becomes larger”, and which is compared with a predetermined threshold value for imbalance determination when the imbalance determination is performed, will also be referred to as an “imbalance determination parameter.”